To understand the fluid dynamics of marine phenomena, fluid-structure interaction problems must be solved. Challenges exist in developing numerical techniques to solve these complex flow problems with boundary conditions at fluid-structure interfaces. I will present details of two problems where these challenges are addressed: (1) modeling of pulsating soft corals and (2) accurate evaluation of layer potentials near interfaces. The first problem of pulsating soft corals will be motivated by field and experimental work in the marine sciences. I will discuss these related data and provide comparisons with the modeling. For the second problem of accurate evaluation of layer potentials, I will show how classical numerical methods are problematic for evaluations close to boundaries and how newly developed numerical methods based on asymptotics can be used to improve accuracy.